#fourier

Topics tagged "fourier".

• Fourier Series

  A periodic signal is an exact sum of harmonics — sinusoids at integer multiples of one fundamental frequency.

• Fourier Transform

  The generalization of the Fourier series to non-periodic signals — an integral that resolves any signal into a continuous band of frequencies.

• Fourier Analysis

  Any signal is a sum of pure sinusoids — and reading it as such turns the tangled language of time into the clean language of frequency.

• Frequency Domain

  The second of the two equivalent views of a signal — describing it by which frequencies it contains rather than by how it varies in time.

• Harmonics

  The integer multiples of a fundamental frequency whose relative strengths give every sound its characteristic color.

• Spectrum

  The magnitude of a signal's frequency content — the map of where its energy lives, read as a landscape of peaks.

• Gibbs Phenomenon

  The persistent ~9% overshoot that a truncated Fourier sum makes near a jump discontinuity — and that never goes away no matter how many terms you add.

• Discrete Fourier Transform

  The Fourier transform of sampled data — and the Nyquist limit and aliasing that sampling forces upon us.

• Convolution

  The sliding-overlap operation that blends two signals — and which, magically, becomes simple multiplication in the frequency domain.

• Uncertainty Principle

  A signal cannot be sharply localized in both time and frequency at once — the tighter one view, the broader the other.